10/23 Lesson 11-3 Arithmetic Sequences as Functions

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n-1)d \), where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Front

What is the common difference in the sequence 11, 23, 35, 47?

Back

The common difference is 12, calculated as \( 23 - 11 = 12 \).

Front

Write the function for the arithmetic sequence 6.5, 9, 11.5, 14.

Back

The function is given by \( f(n) = 2.5n + 4 \).

Front

What ordered pair represents the nth term of the arithmetic sequence 1, 4, 7, 10?

Back

The ordered pair is (n, 3n - 2).

Front

What is the nth term of the sequence 1, 4, 7, 10?

Back

The nth term is given by \( a_n = 3n - 2 \).

Front

How do you determine the function from a graph of an arithmetic sequence?

Back

To determine the function from a graph, identify the slope (common difference) and the y-intercept, then use the linear function format \( f(n) = mn + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Front

What is the formula for the sum of the first n terms of an arithmetic sequence?

Back

The sum of the first n terms can be calculated using the formula: \( S_n = \frac{n}{2} (a_1 + a_n) \), where \( a_1 \) is the first term and \( a_n \) is the nth term.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

Back

The 10th term is \( a_{10} = 5 + (10-1) \cdot 3 = 32 \).

Front

What is the relationship between the terms in an arithmetic sequence?

Back

Each term can be expressed as the previous term plus the common difference.